But despite May's appeal at an EU summit in Austria, EU Council President Donald Tusk insisted that parts of her offer are still not satisfactory more than 18 months into the negotiations and must change to keep alive hopes of concluding a Brexit deal in coming weeks.
Britain leaves the EU at midnight on March 29 — the first time a country has ever left the world's biggest trading bloc — but solutions to outstanding Brexit issues must be found by November so parliaments have time to ratify any accord.
May told reporters that her offer to solve the border riddle — the biggest obstacle to a deal — was "the only credible and negotiable plan on the table that delivers no hard border in Northern Ireland and also delivers on the vote of the British people" to leave the EU.
"If we are going to achieve a successful conclusion then, just as the U.K. has evolved its position, the EU will need to evolve its position too," she said. Tusk, though, highlighted shortfalls in Britain's position on avoiding a hard border, as well as on economic cooperation, saying that "the U.K.'s proposals will need to be reworked and further negotiated."
He ramped up pressure on May — already struggling to keep her job and control in-fighting within her Conservative Party — by saying that time was fast running out. "Every day that is left we must use for talks," Tusk said. He said he wants a deal finalized this autumn, and urged leaders to hold another summit in mid-November as part of a roadmap to get the job done.
Right from the start, both sides pledged to ensure there's no hard border around Northern Ireland but they disagree on how to get there. The EU has offered to effectively keep Northern Ireland in its customs union. EU chief Brexit negotiator Michel Barnier says that could be done by checking goods destined for Northern Ireland at companies and markets within the U.K.
But London says this would undermine the U.K. by treating Northern Ireland differently from the rest of the country. May's latest plan — the so-called Chequers proposals — envisions the whole U.K., including Northern Ireland, remaining in the European single market for goods only, thereby eliminating the need for a hard border.
"We have always recognized that there are unique circumstances that apply in Northern Ireland," May said. "But what we cannot accept is seeing Northern Ireland carved away from the U.K. customs territory because regardless of where the checks would be, what that would mean would be that it would be a challenge to our constitutional and economic integrity."
Earlier this week, Barnier warned that an EU leaders' summit on Oct. 18 in Brussels would be "the moment of truth" for Brexit. Austrian Chancellor Sebastian Kurz, the host of the Salzburg summit, backed May in saying that "both sides need to compromise." However, he said he hoped she would offer "a step forward" during the informal dinner talks Wednesday.
"We have to do everything to avoid a hard Brexit," he said. As the pressure mounts, German Chancellor Angela Merkel noted that Brexit negotiations are "entering the crucial phase." She said Britain's 27 EU partners would discuss May's concerns without her present on Thursday, and Merkel expressed hopes for "an exit that takes place in a good atmosphere, in great respect for each other and that — in certain areas — very, very close cooperation is possible."
Lawless reported from London. Gregory Katz in London and Frank Jordans in Berlin contributed.